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Math Help - Functions

  1. #1
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    Exclamation Functions

    Question:
    Find  \frac{f(x+h)-f(x)}{h} where h is not equal to zero and  f(x)=\sqrt{x} .

    Attempt:
    = \frac{\sqrt{x+h}-\sqrt{x}}{h}
    I have to rationalize the numrator
     = \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{  x}}

    Now how to simplify?

    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question:
    Find  \frac{f(x+h)-f(x)}{h} where h is not equal to zero and  f(x)=\sqrt{x} .

    Attempt:
    = \frac{\sqrt{x+h}-\sqrt{x}}{h}
    I have to rationalize the numrator
     = \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{  x})}

    Now how to simplify?

    Thank you
    \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{  x})}=\frac{1}{(\sqrt{x+h}+\sqrt{x})}
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